Hostname: page-component-8448b6f56d-dnltx Total loading time: 0 Render date: 2024-04-19T22:18:15.933Z Has data issue: false hasContentIssue false

Pairwise concepts in bitopological spaces

Published online by Cambridge University Press:  09 April 2009

Sunder Lal
Affiliation:
Institute of Advanced Studies, Meerut University, Meerut 250001 India.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Several pairwise concepts have been studied for bitopological spaces. In this note an attempt has been made to see how much ‘bitopological’ these pairwise concepts are. For example pairwise T1 is purely a topological concept whereas pairwise normality is very much ‘bitopological’. Several questions pertaining to this theme are dealt with.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1978

References

Birsan, T. (1969), Compacite dans les espaces bitopologique,’ An St. Univ. Iasi Matematica 15 page 2 317328.Google Scholar
Cooke, I. E. and Reilly, I. L. (1975), ‘On bitopological compactness’, J. London Math. Soc. 8, 518522.CrossRefGoogle Scholar
Dutta, M. C. (1971), ‘Contributions to the theory of Bitopological Spaces’ (Thesis) B.I.T.S. Pilani.Google Scholar
Fletcher, P., Hoyle, H. B. and Patty, C. W. (1969), ‘Comparison of topologies’, Duke Math. J. 36 325331.CrossRefGoogle Scholar
Kelly, J. C. (1963), ‘Bitopological spaces’, Proc. London Math. Soc. 13, 7189.CrossRefGoogle Scholar
Kim, Y. W. (1968), ‘Pairwise compactness’, Publ. Math. 15, 8790.Google Scholar
Lane, E. P. (1967), ‘Bitopological spaces and quasi-uniform spaces’, Proc. London Math. Soc. 17, 241256.CrossRefGoogle Scholar
Murdeshwar, M. G. and Naimpally, S. A. (1966), Quasi-uniform Topological Spaces, Monograph Noordhoof Ltd.Google Scholar
Patty, C. W. (1967), ‘Bitopological spaces’, Duke Math. J. 34, 387392.CrossRefGoogle Scholar
Pervin, W. J. (1967), ‘Connectedness in bitopological spaces’, Indag. Math. 29, 369372.CrossRefGoogle Scholar
Reilly, I. L. (1972), ‘On bitopological separation properties’, Nanta Math. 5, 1425.Google Scholar
Reilly, I. L. (1973), ‘Pairwise Lindelöf bitopological spaces’, Kyungpook Math. J. 13, 14.Google Scholar
Saegrove, M. J. (1973), ‘Pairwise complete regularity and compactification in bitopological spaces’, J. London Math. Soc. 7, 286290.CrossRefGoogle Scholar
Singal, M. K. and Jain, S. C. (unpublished), ‘On separation axioms weaker than pairwise Hausdorft’.Google Scholar
Singal, M. K. and Singal, A. R. (1970), ‘Some more separation axioms in bitopological spaces’, Ann. de la Soc. Sc. de Brux. 84, 207230.Google Scholar
Swart, J. (1971), ‘Total disconnectedness in bitopological spaces and product bitopological spaces’, Indag. Math. 33, 135145.CrossRefGoogle Scholar